What three numbers have an average of 401?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 401. This means if we add these three numbers together and divide by 3, we should get 401.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 401 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 401 * 3 = x + y + z
- So, the sum of our three numbers should be: 1203
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1203.
Solution 1:
401, 401, 401
Verification:
(401 + 401 + 401) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 2:
401, 401, 401
Verification:
(401 + 401 + 401) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 3:
1089, 3, 111
Verification:
(1089 + 3 + 111) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 4:
384, 553, 266
Verification:
(384 + 553 + 266) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Solution 5:
578, 375, 250
Verification:
(578 + 375 + 250) / 3 = 1203 / 3 ≈ 401
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 1203 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.